Example of mathematics in Markdown

This post is a small check that the website can now render mathematical expressions written in Markdown. The idea comes from Algebrica, where entries combine ordinary text with LaTeX for inline and display formulas.

An inline expression can be written with $...$ delimiters, as in Algebrica: $f(x) = x^2 + 1$. The \(...\) form also works, for example $e^{i\pi} + 1 = 0$. The result is integrated into the paragraph without needing images.

For display equations, $$ can be used:

$$\int_0^1 x^2 \, dx = \frac{1}{3}$$

Multi-line expressions work too:

$$\begin{aligned} F(x) &= \int 3x^2 \, dx \\ &= x^3 + c \end{aligned}$$

And it is possible to write slightly denser identities, such as the closed form of the geometric sum:

$$\sum_{k=0}^{n} ar^k = \begin{cases} a(n + 1), & r = 1 \\ a \dfrac{1-r^{n+1}}{1-r}, & r \ne 1 \end{cases}$$

The page loads the KaTeX stylesheet only because this post declares math: true in the front matter.